Use elimination to solve the system of equations. 11f+14g=1311𝑓+14𝑔=13 11f+10g=25

Step 1: Write down the system of equations

The system of equations is:

11f + 14g = 13 11f + 10g = 25

Step 2: Subtract the second equation from the first

To eliminate f, we subtract the second equation from the first:

(11f + 14g) - (11f + 10g) = 13 - 25

This simplifies to:

4g = -12

Step 3: Solve for g

To solve for g, we divide both sides of the equation by 4:

g = -12 / 4 = -3

Step 4: Substitute g = -3 into the first equation

Substituting g = -3 into the first equation gives us:

11f + 14(-3) = 13

This simplifies to:

11f - 42 = 13

Step 5: Solve for f

To solve for f, we add 42 to both sides of the equation and then divide by 11:

f = (13 + 42) / 11 = 55 / 11 = 5

So, the solution to the system of equations is f = 5 and g = -3.